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CA Foundation · Quantitative Aptitude · Linear Inequalities

The solution of 4(x − 1) − 3(2x + 1) ≥ 5 for real x is:

The solution is x ≤ −6. Expanding gives −2x − 7 ≥ 5, so −2x ≥ 12. Dividing by the negative number −2 reverses the inequality sign, so x is at most −6.

  1. Ax ≥ −6
  2. Bx ≤ −6Correct
  3. Cx ≤ −2
  4. Dx ≥ 6

Explanation

Expand: 4x − 4 − 6x − 3 ≥ 5, so −2x − 7 ≥ 5. Then −2x ≥ 12. Dividing by −2 reverses the sign, giving x ≤ −6. Option 1 forgets to reverse the sign.

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